Scattering of flexural waves by a semi-infinite crack in an elastic plate carrying an electric current

Smart structures are components used in engineering applications that are capable of sensing or reacting to their environment in a predictable and desired manner. In addition to carrying mechanical loads, smart structures may alleviate vibration, reduce acoustic noise, change their mechanical properties as required or monitor their own condition. With the last point in mind, this article examines the scattering of flexural waves by a semi-infinite crack in a non-ferrous thin plate that is subjected to a constant current aligned in the direction of the crack edge. The aim is to investigate whether the current can be used to detect or inhibit the onset of crack growth. The model problem is amenable to an exact solution via the Wiener–Hopf technique, which enables an explicit analysis of the bending (and twisting) moment intensity factors at the crack tip, and also the diffracted field. The latter contains an edge wave component, and its amplitude is determined explicitly in terms of the current and angle of incidence of the forcing flexural wave. It is further observed that the edge wave phase speed exhibits a dual dependence on frequency and current, resulting in two distinct asymptotic behaviours.